Discussion of Homotopy Type Theory and Univalent Foundations
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From: Thomas Streicher <stre...@mathematik.tu-darmstadt.de>
To: Thorsten Altenkirch <Thorsten....@nottingham.ac.uk>
Cc: Andrej Bauer <andrej...@andrej.com>,
	Homotopy Type Theory <homotopyt...@googlegroups.com>
Subject: Re: [HoTT] Impredicative set + function extensionality + proof irrelevance consistent?
Date: Tue, 19 Dec 2017 16:31:18 +0100	[thread overview]
Message-ID: <20171219153118.GA9218@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <A336FB3E-8247-4240-A034-3119B1C516FB@exmail.nottingham.ac.uk>

>     Furthermore, there can be class-many subobjects of 1 in a topos, for
>     instance in sets there are class-many singletons. Of course, a whole
>     lot of them will be isomorphic and very many "correspond to" the
>     element ??? : ??. But at least on this mailing list we're not in the
>     business of sweeping isomorphisms under the rug.

Thanks, Andrej, for trying to clean up the discussion!

Thorsten hads not daid how to inetrpret equality. In an arbitrary
topos there is no other choice than interpeting equality by fibrewise
diagonals. So we have extensional equality!

I am afraid there want exist too many univalent categories. They all
would be rigid which is very inconstructive.

Thomas

  reply	other threads:[~2017-12-19 15:31 UTC|newest]

Thread overview: 54+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2017-12-11  4:22 Kristina Sojakova
2017-12-11 11:42 ` [HoTT] " Jon Sterling
2017-12-11 12:15   ` Kristina Sojakova
2017-12-11 12:43     ` Jon Sterling
2017-12-11 14:28       ` Thomas Streicher
2017-12-11 14:32         ` Kristina Sojakova
2017-12-11 14:23 ` Thorsten Altenkirch
2017-12-12 10:15   ` Andrea Vezzosi
2017-12-12 11:03     ` Thorsten Altenkirch
2017-12-12 12:02       ` Thomas Streicher
2017-12-12 12:21         ` Thorsten Altenkirch
2017-12-12 13:17           ` Jon Sterling
2017-12-12 19:29             ` Thomas Streicher
2017-12-12 19:52               ` Martin Escardo
2017-12-12 23:14           ` Michael Shulman
2017-12-14 12:32             ` Thorsten Altenkirch
2017-12-14 18:52               ` Michael Shulman
2017-12-16 15:21                 ` Thorsten Altenkirch
2017-12-17 12:55                   ` Michael Shulman
2017-12-17 17:08                     ` Ben Sherman
2017-12-17 17:16                       ` Thorsten Altenkirch
2017-12-17 22:43                         ` Floris van Doorn
2017-12-15 17:00           ` Thomas Streicher
2017-12-17  8:47             ` Thorsten Altenkirch
2017-12-17 10:21               ` Thomas Streicher
2017-12-17 11:39                 ` Thorsten Altenkirch
2017-12-18  7:41                   ` Matt Oliveri
2017-12-18 10:00                     ` Michael Shulman
2017-12-18 11:55                       ` Matt Oliveri
2017-12-18 16:24                         ` Michael Shulman
2017-12-18 20:08                           ` Matt Oliveri
2017-12-18 10:10                     ` Thorsten Altenkirch
2017-12-18 11:17                       ` Matt Oliveri
2017-12-18 12:09                       ` Matt Oliveri
2017-12-18 11:52                   ` Thomas Streicher
2017-12-19 11:26                     ` Thorsten Altenkirch
2017-12-19 13:52                       ` Andrej Bauer
2017-12-19 14:44                         ` Thorsten Altenkirch
2017-12-19 15:31                           ` Thomas Streicher [this message]
2017-12-19 16:10                             ` Thorsten Altenkirch
2017-12-19 16:31                               ` Thomas Streicher
2017-12-19 16:37                                 ` Thorsten Altenkirch
2017-12-20 11:00                                   ` Thomas Streicher
2017-12-20 11:16                                     ` Thorsten Altenkirch
2017-12-20 11:41                                       ` Thomas Streicher
2017-12-21  0:42                                         ` Matt Oliveri
2017-12-22 11:18                                           ` Thorsten Altenkirch
2017-12-22 21:20                                             ` Martín Hötzel Escardó
2017-12-22 21:36                                               ` Martín Hötzel Escardó
2017-12-23  0:25                                               ` Matt Oliveri
2017-12-19 16:41                         ` Steve Awodey
2017-12-20  0:14                           ` Andrej Bauer
2017-12-20  3:55                             ` Steve Awodey
     [not found]       ` <fa8c0c3c-4870-4c06-fd4d-70be992d3ac0@skyskimmer.net>
2017-12-14 13:28         ` Thorsten Altenkirch

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